Call it the couponing of higher education. After years of skyrocketing tuition costs, many private colleges in the United States are ramping up their financial aid packages in an attempt to attract new students and boost sagging enrollments.

For freshmen entering school in 2012, the average “tuition discount rate” – the amount of grant and scholarship money given by schools toward tuition – was 45%, an all-time high, according to a survey of 383 private, non-profit four-year colleges released Monday by the National Association of College and University Business Officers (NACUBO). Those substantial discounts, offered in the form of merit scholarships and need-based aid, are meant to lure cash-strapped students who might not otherwise think of private schools as a viable financial option.

“Institutions are responding to students who won’t enroll unless they have some kind of incentive,” says Natalie Pullaro Davis, who wrote the survey report. “Schools are foregoing more of their revenue in order to fill seats and be sensitive to families who are struggling.” As a result, these schools bring in only about 55 cents of every tuition dollar they charge. But as Pullaro Davis said, “It’s better to collect some money on a seat, than to collect no money.”

And many of these colleges do indeed have to worry about having empty seats come fall. The survey found that total undergraduate enrollments in 2012 were down 45.6% from the year before. “It’s a tight rope they walk,” said Mark Kantrowitz, an expert on college costs and the publisher of edvisors.com. “If they enroll one student by giving them $10,000 more in aid, that’s $10,000 less that they can give to another student.”

Even with aid at an all-time high, however, families can try to negotiate for a better deal. “If you think there is some aspect of your background that the college didn’t consider, it doesn’t hurt to appeal for more aid,” Kantrowitz said. “You can contact the school and say, ‘You’re my first choice school’—only say that to one school—’and I really want to go, but I can’t figure out how to make it work financially. Is there anything you can do to make it work?'”

Admissions and financial aid officers said that approach is only likely to work if the student’s request is need-based— especially now that they are making increasingly generous merit-based offers upfront. “We don’t go out with a low ball offer and then wait for students to appeal,” said Joe Bagnoli, vice president for enrollment and dean of admission at Grinnell College, a private liberal arts school in Grinnell, Iowa, that participated in the survey. This year he said the school received about 150 appeals from families looking to increase the amount of aid they were awarded, up from 90 last year.

Similarly, Macalester College, a private liberal arts school in St. Paul, Minn., that also participated in the survey, increased its budget for financial aid by 11% and expanded its merit-based scholarship program in 2009 in order to attract students. “We have a situation where the top students in our admitted student pool are highly qualified and have a lot of good choices for where they can go to school,” said Brian Lindeman, Macalester’s director of financial aid. “If we’re able to offer a scholarship, we have a better chance of being one of their top choices.”

Both Macalester and Grinnell said they only reconsider awards if the family’s financial situation changed after they filled out the application for aid. “We don’t ask them to fax us their best offer, so we can try to beat it,” Lindeman said. “We try to explain our approach and say we understand they may have a lower cost option. We encourage them to evaluate the value of their choices and decide whether it’s appropriate to spend more to come to Macalester.”

At least one school is eschewing the coupon model in favor of a single, set price. Requests to match merit aid from other schools used to be common at the University of the South in Sewanee, Tenn., said John McCardell, the school’s vice chancellor. Two years ago the school changed its approach, cutting tuition by 10%, locking in a four-year price for incoming students, and ending the practice of negotiating academic scholarships. Those negotiations, McCardell said, “put us in an uncomfortable position where we would wonder if we were simply being used to get a better deal from the place up the road. Now if a family wants to bicker, they can go bicker somewhere else.”